Gaussian / Statistical Threshold Models

Best for: Simple monitoring

How it works

Assumes normal observations follow a fixed distribution, classically a Gaussian $\mathcal{N}(\mu,\sigma^2)$, and flags deviations exceeding a critical threshold via the z-score $z=\frac{x-\mu}{\sigma}$ (typically $|z|>3$). The multivariate generalisation uses the Mahalanobis distance $d^2=(x-\mu)^\top\Sigma^{-1}(x-\mu)$, which accounts for correlations and reduces to a $\chi^2$ test under normality. Cheap and interpretable, but fragile when the data is non-Gaussian or non-stationary.

Common fields

DevOps · finance · process control